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Title:  Inequalities for the differential subordinates of Martingales, harmonic functions and Ito processes 
Author(s):  Choi, Changsun 
Doctoral Committee Chair(s):  Ruan, ZhongJin 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  In Chapter 1 we sharpen Burkholder's inequality $\mu(\vert v\vert\geq1)\leq2\Vert u\Vert\sb1$ for two harmonic functions u and v by adjoining an extra assumption. That is, we prove the weaktype inequality $\mu(\vert v\vert\geq1)\leq K\Vert u\Vert\sb1$ under the assumptions that $\vert v(\xi)\vert\leq\vert u(\xi)\vert, \vert\nabla v\vert\leq\vert\nabla u\vert$ and the extra assumption that $\nabla u\cdot\nabla v$ = 0. Here $\mu$ is the harmonic measure with respect to $\xi$ and the constant 1 $

Issue Date:  1995 
Type:  Text 
Language:  English 
URI:  http://hdl.handle.net/2142/19178 
Rights Information:  Copyright 1995 Choi, Changsun 
Date Available in IDEALS:  20110507 
Identifier in Online Catalog:  AAI9624313 
OCLC Identifier:  (UMI)AAI9624313 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Mathematics